HARMONY IN MUSIC. 57 



impossibility. Such performers may aspire to three whole 

 octaves lying above the five-accented c, and very painful to the 

 ear, for their existence has been established by Despretz, who, 

 by exciting small tuning-forks with a violin bow, obtained and 

 heard the eight-accented c, having 32,770 vibrations in a second. 

 Here the sensation of tone seemed to have reached its upper 

 limit, and the intervals were really undistinguishable in the 

 later octaves. 



The musical pitch of a tone depends entirely on the number 

 of vibrations of the air in a second, and not at all upon the 

 mode in which they are produced. It is quite indifferent whether 

 they are generated by the vibrating strings of a piano or violin, 

 the vocal chords of the human larynx, the metal tongues of the 

 harmonium, the reeds of the clarionet, oboe, and bassoon, the 

 trembling lips of the trumpeter, or the air cut by a sharp edge 

 in organ pipes and flutes. 



A tone of the same number of vibrations has always the 

 same pitch, by whichever one of these instruments it is pro- 

 duced. That which distinguishes the note A of a piano, for 

 example, from the equally high A of the violin, flute, clarionet, 

 or trumpet, is called the quality of the tone, and to this we shall 

 have to recur presently. 



As an interesting example of these assertions, I beg to show you a 

 peculiar physical instrument for producing musical tones, called the 

 siren, Fig. 1, which is especially adapted to establish the properties 

 resulting from the ratios of the numbers of vibrations. 



In order to produce tones upon this instrument, the portvents g 

 and gj are connected by means of flexible tubes with a bellows. The 

 air enters into round brass boxes, a and a^ and escapes by the per- 

 forated covers of these boxes at c and c,. But the holes for the 

 escape of air are not perfectly free. Immediately before the covers 

 of both boxes there are two other perforated discs, fastened to a per- 

 pendicular axis k, which turns with great readiness. In the figure, 

 only the perforated disc can be seen at c , and immediately below it 

 is the similarly perforated cover of the box. In the upper box, c ]? 

 only the edge of the disc is visible. If then the holes of the disc are 

 precisely opposite to those of the cover, the ah- can escape freely. 

 But if the disc is made to revolve, so that some of its unperforated 



